Monte Carlo simulation of normal grain growth in 2- and 3-dimensions: the lattice-model-independent grain size distribution

The phenomenon of normal grain growth in pure single phase systems is modeled with the Monte Carlo technique and a series of simulations are performed in 2- and 3-dimensions. The results are compared with natural and experimental monomineralic rock samples. In these simulations various lattice models with different anisotropic features in grain boundary energy are examined in order to check the universality of the simulation results. The obtained microstructure varies with the artificial parameter T′ in each lattice model, where T′ means scaled temperature and controls thermal fluctuation on grain boundary motion. As T′ (thermal fluctuation) increases, the boundary energy anisotropy characterizing each lattice model becomes less important for the evolution of the microstructure. As a result the difference in the grain size distribution among the lattice models, which is significantly large for low T′, is reduced with increasing T′. The distribution independent of both the lattice model and the dimension is obtained at sufficiently high T′ and is very close to the normal distribution when carrying out the weighting procedure with a weight of the square of each grain radius. A comparison of the planar grain size distribution of the natural and experimental rock samples with the 3-D simulation results reveals that the simulations reproduce very well the distributions observed in the real rock samples. Although various factors such as the presence of secondary minerals and a fluid phase, which are not included in the simulation modeling, are generally considered to influence the real grain growth behavior, the good agreement of the distribution indicates that the overall grain growth behavior in real rocks may still be described by the simplified model used in the present simulations. Thus the grain size distribution obtained from the present simulations is possessed of the universal form characterizing real normal grain growth of which the driving force is essentially grain boundary energy reduction through grain boundary migration.